Augustin Louis Cauchy
|
Augustin Louis Cauchy | |
|---|---|
 Augustin Louis Cauchy | |
| Born |
August 21 1789 |
| Died | 23 May 1857 |
| Residence |  France
|
| Nationality | French
|
| Field | calculus |
| Institutions | École Centrale du Panthéon École Nationale des Ponts et Chaussées École polytechnique |
| Alma mater | École Nationale des Ponts et Chaussées |
| Known for | Cauchy integral theorem |
| Religious stance | Catholic |
Augustin Louis Cauchy (August 21, 1789 – May 23,1857) was a French mathematician. He started the project of formulating and proving the theorems of calculus in a rigorous manner and was thus an early pioneer of analysis. He applied higher mathematics to the solution of problems in physics. Cauchy was a great educator who devoted much of his life to teaching and writing treatises on calculus. He was a devout Catholic, and toward the end of his life, devoted as much of his time to charitable works as to his professional duties.
Biography
Early life
Cauchy received his early education from his father Louis François Cauchy, an archivist for the French Senate. The elder Cauchy's position brought him into contact with many of the leaders of his age, including the mathematician Joseph Louis Lagrange, who personally took an interest in his son's early education. Lagrange advised his father to educate Cauchy in the classics before exposing him to mathematical studies.
Two of Cauchy's brothers would carve out reputations for themselves. Alexandre Laurent Cauchy became a president of a division of the court of appeal and a judge of the court of cassation. Eugène François Cauchy was a publicist who also wrote several mathematical works.
At the outset of the French Revolution, Cauchy's father was forced to flee with the family to Arcueil during the French Revolution. Their life there was apparently hard and Cauchy spoke of living on rice, bread, and crackers during the period. This instilled in Cauchy a strong affinity to the monarchy and a distain for the republican form of government brought about by the revolution.
University education
Cauchy entered the École Centrale du Panthéon in 1802, placing first in Latin and Greek verse and second in Latin composition. He left the school in 1804, and studied mathematics in preparation for the entrance examinations for the Ecole Polytechnique, in which he ranked second. He entered the Polytechnique in 1805, and the École Nationale des Ponts et Chaussées in 1807. Having adopted the profession of an engineer, he left Paris for Cherbourg in 1810, but returned in 1813 on account of his health, whereupon Lagrange and Pierre-Simon Laplace persuaded him to renounce engineering and to devote himself to mathematics.
Early work
The genius of Cauchy was perhaps first illustrated in his simple solution of the problem of Apollonius, that is, to describe a circle touching three given circles, which he discovered in 1805. In 1811, Cauchy added to this accomplishment through his generalization of Euler's formula on polyhedra, and by the solutions to several other elegant problems.
In 1815, Cauchy won the Grand Prix of the Institute of France for his solution to the problem of waves produced at the surface of a liquid of indefinite depth, beating out the esteemed mathematician Poisson. The following year, he was admitted as a member of the French Academy of Sciences after the departure of Gaspard Monge and Lazare Carnot, two well respected members who lost their places because of strong ties with Napoleon's government, which had by then relinquished power to the bourbon monarchy. This generated tension between Cauchy and some members of the French scientific community.
Cauchy became assistant professor of analysis at the École Polytechnique in 1815, and was promoted to titular professor in 1816. In 1818 he married Aloise de Bure, with whom he had two daughters. His wife was a close relative of a publisher who published most of Cauchy's works.
In the 1820s, Cauchy published the fruits of his teaching labors several major treatises. These included Cours d'analyse de l'École Polytechnique (1821); Le Calcul infinitésimal (1823); Leçons sur les applications de calcul infinitésimal; La géométrie (1826–1828); and also in his Courses of mechanics (for the École Polytechnique), Higher algebra (for the Faculté des Sciences), and of Mathematical physics (for the Collège de France).
In 1826, he launched a periodical, Mathematical Exercises, devoted entirely to his own work. This publication continued, with intermittent interruptions, until Cauchy's death, and inspired many fruitful investigations by later researchers.
Middle years
In 1830, on the accession of Louis-Philippe, he refused to take an oath of allegiance to the new government, and relinquished his position at the Polytechnique. A short sojourn at Fribourg in Switzerland was followed by his appointment in 1831 to the newly-created chair of mathematical physics at the University of Turin.
In 1833 the deposed king Charles X of France summoned Cauchy to be tutor to his grandson, the duke of Bordeaux, an appointment which enabled Cauchy to travel and thereby become acquainted with the favourable impression which his investigations had made. Physicist Amadeo Avogadro assumed the Turin professorship vacated by Cauchy.
Charles X conveyed to Cauchy the title and privileges of a baron in return for his services. Returning to Paris in 1838, Cauchy refused a proffered chair at the Collège de France because an oath of allegiance to the throne was required. He was proposed for a post at the Bureau of Longitudes in 1839, but he likewise refused to take an oath, and, in spite of backing from friends and colleagues, lost the appointment. But in 1848, the oath having been suspended, he resumed his post at the École Polytechnique. In 1851, after the coup d'état of that year, Cauchy and François Arago were exempted from taking an oath. Subequently, Cauchy lived in the France ruled by the emperor Napoleon III until his death.
Later life
Much of Cauchy's efforts in later years were devoted to religious and charitable works. When he was 53, he learned Hebrew in order to help his father with some religious researches. Toward the end of his life, Cauchy donated a large part of his income from the state to charitable purposes, and was engaged in other works of mercy. The mayor of Sceaux, where Cauchy made his home, said that Cauchy "had two distinct lives: the Christian and the scientific life, each so full, so complete, that it would have served to confer luster on any name." In 1856, when the mathematician Charles Hermite contracted small pox, it was Cauchy who nursed him back to health, and persuaded him to embrace the Catholic faith.
In the field of mathematics, Cauchy was active until a few days before his death. In a paper published in 1855, he discussed some theorems, one of which is similar to the "Argument Principle" in many modern textbooks on complex analysis. In modern control theory textbooks, the Cauchy argument principle is quite frequently used to derive the Nyquist stability criterion, which can be used to predict the stability of negative feedback amplifier and negative feedback control systems.
In May of 1857, he submitted a memoir to the academy on a technique for astronomical calculations. A week later he attended a session of the academy, but was suffering from a cold. His symptoms became more severe, affecting his appearance and mobility. A cleric is said to have warned Cauchy to slow his work pace, so that the prayers of the faithful on his behalf would bare fruit. But he said in response: "Dear sir, men pass away, but their works remain. Pray for the work."
Cauchy retreated to his residence at Sceaux, and remained there, continuing to work on the theory of series. As late as the 21st of May, he conversed with the archbishop of Paris, although in a considerably enfeebled condition. Two days later, on May 23, 1857, he awoke at three in the morning, only to expire half an hour later. His last words are said to have been a reference to the great figures of Catholic belief, Jesus, Mary and Joseph.
Work
Cauchy made 789 contributions to scientific journals. These writings covered notable topics including the theory of series (where he developed with perspicuous skill the notion of convergency), the theory of numbers and complex quantities, the theory of groups and substitutions, and the theory of functions, differential equations and determinants.
He clarified the principles of the calculus by developing them with the aid of limits and continuity, and was the first to prove rigorouslyTaylor's theorem which demonstrates the manner in which a function can be represented by an infinite series whose terms contain derivatives of the function at a point. In doing so, he laid down his well-known form of the remainder, the difference in value between the sums of a finite and an infinite number of terms of a series. He also contributed significant research in mechanics, substituting the notion of the continuity of geometrical displacements for the principle of the continuity of matter. In optics, he developed the wave theory, and his name is associated with the simple dispersion formula. In elasticity, he originated the theory of stress, and his results are nearly as valuable as those of Simeon Poisson.
Other significant contributions include being the first to prove the Fermat polygonal number theorem. His collected works, Œuvres complètes d'Augustin Cauchy, have been published in 27 volumes.
Character and legacy
Cauchy was unusual in that he left not only a body of work of monumental proportions, but also the path of a life devoted to good works. At the same time, he appears to have often been disputatious, sparing with fellow mathematicians, sometimes denying them credit for their work, and on occasion refusing to admit to the limitations of his own work. These imperfections were maintained along with an ongoing interest in public beneficence.
Cauchy was a defender of royalism and hence refused to take oaths to any government after the overthrow of Charles X. This reveals him to have been a man of strong convictions and unbending principles.
He was a devout Catholic and a member of the Society of Saint Vincent de Paul. He also had links to the Society of Jesus and defended them at the Academy when it was politically unwise to do so. His zeal for his faith may have led to his caring for the mathematician Charles Hermite and inspired him to plea on behalf of the Irish during the Potato Famine.
His royalism and religious zeal also made him contentious, which caused difficulties with his colleagues. He felt that he was mistreated for his beliefs, but his opponents felt he intentionally provoked people by berating them over religious matters or by defending the Jesuits after they had been suppressed. Niels Henrik Abel denounced his stubbornness but praised him as a mathematician. Cauchy's views were widely unpopular among mathematicians, and when Guglielmo Libri Carucci dalla Sommaja was made chair in mathematics before him he, and many others, felt his views were the cause. When Libri was accused of stealing books he was replaced by Joseph Liouville which caused a rift between him and Cauchy. Another dispute concerned Jean Marie Constant Duhamel and a claim on inelastic shocks. Cauchy was later shown, by Jean-Victor Poncelet, that he was in the wrong. Despite that Cauchy refused to concede this and nursed a bitterness on the whole issue.
Still, Cauchy's great contributions to mathematics, and his devotion to teaching as reflected in his important treatises, trivialize the disputes with others he had during his lifetime.
See also
- Cauchy integral theorem
- Cauchy's integral formula
- Cauchy-Schwarz inequality
- Cauchy's theorem (group theory)
- Cauchy's theorem (geometry)
- Cauchy distribution
- Cauchy determinant
- Cauchy formula for repeated integration
- Cauchy sequence
- Cauchy-Riemann equations
- Cauchy-Frobenius lemma
- Cauchy product
- Cauchy principal value
- Cauchy-Binet formula
- Cauchy-Euler equation
- Cauchy's equation
- Cauchy problem
- Cauchy horizon
- Cauchy boundary condition
- Cauchy surface
- Cauchy-Kovalevskaya theorem
- Maclaurin-Cauchy test
- Cauchy's radical test
- Cauchy (crater)
- Cauchy functional equation
- Cauchy-Peano theorem
- Cauchy argument principle
- Nyquist stability criterion
ReferencesISBN links support NWE through referral fees
- Royal Society (Great Britain). 1854. Proceedings of the Royal Society of London. London: Printed by Taylor and Francis. 45-49.
- Kelland. 1858. Notice of the life and writings of Baron Cauchy, in The Edinburgh new philosophical journal, exhibiting a view of the progressive discoveries and improvements in the sciences and the arts. Edinburgh: A. and C. Black.
- Nickles, Jerome. 1858. Obituary in American journal of science, 2d ser. 1846-70; New-Haven: Converse. 25:91-95.
External links
- Cauchy criterion for convergence. Retrieved September 13, 2007.
- Œuvres complètes d'Augustin Cauchy Académie des sciences (France). Ministère de l'éducation nationale. Retrieved September 13, 2007.
- MacTutor biography. Retrieved September 13, 2007.
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